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Determine the kinetic energy of the planar pendulum of Example 1.1.
EXAMPLE 1.1
Kinematics of a planar pendulum
Consider the planar pendulum shown in Figure 1.3, where the orthogonal unit vectors e_{1} and e_{2} are fixed to the pendulum and they share the motion of the pendulum. The unit vectors i, j, and k, which point along the X, Y and Z directions, respectively, are fixed in time. The velocity and acceleration of the planar pendulum P with respect to point O are the quantities of interest. The position vector from point O to point P is written as
Making use of Eqs. (1.2) and (1.8) and noting that both h and L are constant with respect to time and the angular velocity v , the pendulum velocity is
In arriving at Eqs. (b) and (c), the following relations have been used.
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